Let $G$ be a connected reductive group defined over a non-archimedean local field $F$.
The category $R(G)$ of smooth representations of G(F) has a decomposition into a
product of indecomposable subcategories called Bernstein blocks and to each block is
associated a non-negative real number called Moy-Prasad depth. We will begin with
recalling all this basic theory. Then we will focus the discussion on ‘regular’ blocks.
These are ‘most’ Bernstein blocks when the residue characteristic of $F$ is suitably
large. We will then talk about an approach of studying blocks in $R(G)$ by studying a
suitably related depth-zero block of certain other groups. In that context, I will
explain some results from a joint work with Jeffrey Adler. One of them being that the
Bernstein center (i.e., the center of a Bernstein block) of a regular block is isomorphic
to the Bernstein center of a depth-zero regular block of some explicitly describable
another group. I will give some applications of such results.